PHP Program - Calculate sum of Cubes of Natural numbers
In Mathematics, the natural numbers are all positive numbers which is used for counting like 1, 2, 3, 4, and so on. The smallest natural number is 1.
Objective: Write a PHP program which returns sum of cubes of natural numbers starting from 1 to given natural number n, (13 + 23 + 33 + ... + n3).
Method 1: Using while loop
The example below shows how to use while loop to calculate sum of cubes of first n natural numbers.
<?php $n = 10; $i = 1; $sum = 0; //calculating sum of cubes from 1 to n while($i <= $n) { $sum += $i**3; $i++; } echo "Sum is: $sum"; ?>
The above code will give the following output:
Sum is: 3025
Method 2: Using for loop
The same can be achieved using for loop. Consider the example below:
<?php $n = 10; $sum = 0; //calculating sum of cubes from 1 to n for($i = 1; $i <= $n; $i++) $sum += $i**3; echo "Sum is: $sum"; ?>
The above code will give the following output:
Sum is: 3025
Method 3: Using Recursion
Similarly, recursion can be used to calculate the sum.
<?php //recursive function function Sum($n) { if($n == 1) return 1; else return ($n**3 + Sum($n-1)); } echo "Sum of Cubes of first 10 natural numbers: ".Sum(10)."\n"; echo "Sum of Cubes of first 20 natural numbers: ".Sum(20)."\n"; ?>
The above code will give the following output:
Sum of Cubes of first 10 natural numbers: 3025 Sum of Cubes of first 20 natural numbers: 44100
Method 4: Using Mathematical Formula
The sum of cubes of first n natural numbers can be mathematically expressed as:
<?php $n = 10; //calculating sum of cubes from 1 to n $sum = $n*($n+1)/2; $sum **= 2; echo "Sum is: $sum"; ?>
The above code will give the following output:
Sum is: 3025
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